Simulate random paths

Load libraries

library(tidyverse)
library(plotly)

Make function to simulate paths

SimPath <- function(startvalue=100, meangrowth=0.1, sd=0.01, iterations=10) {
  
  i <- 0
  sim <- c(i)
  values <- c(startvalue)
  
  while(i < iterations) {
    i <- i+1
    sim <- c(sim, i)
    g <- rnorm(1, meangrowth, sd)
    values <- c(values, values[i]*(1+g))
  }
  return(data.frame(sim, values))
}
SimPath(100, 0.10, 0.01, 3)

Create graphs

# Input data
mean <- 0.30
sd <- 0.20
t <- 8
expval <- 100*(1+mean)^t
expDF <- data.frame(x=t, y=expval)
# Start calculations
n <- 1
pathsDF <- cbind(run = rep(n,t+1), SimPath(100, mean, sd, t))
while(n < 400) {
  n <- n + 1
  run <- rep(n,t+1)
  pathsDF <- rbind(pathsDF, cbind(run, SimPath(100, mean, sd, t)))
  
}
pathsDF$run <- as.factor(pathsDF$run)
p <- ggplot() +
  geom_line(data = pathsDF, aes(x=sim, y=values, group=run), colour="Red", alpha=1/10) +
  geom_point(data = expDF, aes(x=x, y=y, text="Expected end value"), colour = "RoyalBlue", size=3) +
  theme(legend.position="none")
ggplotly(p)